Introduction

There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such as the psychology of reasoning and mathematics education. This introduction offers a snapshot of each trend and addresses how they intersect with some of the standard criticisms of experimental philosophy. It also briefly summarizes the specific contribution of the other chapters of this book

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

The Complexity Era in Economics

This article argues that the neoclassical era in economics has ended and is being replaced by a new era. What best characterizes the new era is its acceptance that the economy is complex, and thus that it might be called the complexity era. The complexity era has not arrived through a revolution. Instead, it has evolved out of the many strains of neoclassical work, along with work done by less orthodox mainstream and heterodox economists. It is only in its beginning stages. The article discusses the work that is forming the foundation of the complexity era, and how that work will likely change the way in which we understand economic phenomena and the economics profession.

A Rational Irrational Man

A man is a key subject of economics and economic theory. “A man is irrational” - this opinion can be made from Allais paradox, risk aversion and other well-known fundamental problems. For a long time, this opinion was a barrier to proper solution of these problems and the development of the economic theory. A radically new approach has been proposed. It considers arrangement infringement possibility as a quite different source of such problems. It opens a quite different way to solve them and remove this barrier. It helps economists to open new and rediscover old fields and trends for the research.“non-ideal” economics, risk, market, bank, industry, development

A Rational Irrational Man?

A man is a key subject of economics. “A man is irrational” - this opinion can be made from Allais paradox, risk aversion and other well-known fundamental problems. For a long time, this opinion was a barrier to proper solution of these problems and the development of the economics. A radically new way is proposed to solve them and remove this barrier. The way is the generalization of a breach of a term of contract.risk, business, bank, trade, industry, development, utility, contract, “ideal” economics, investment